Cyclic colorings of plane graphs with independent faces

Let G be a plane graph with maximum face size Δ^∗. If all faces of G with size four or more are vertex disjoint, then G has a cyclic coloring with Δ^∗+1 colors, i.e., a coloring such that all vertices incident with the same face receive distinct colors.     

High-Order Parametric Polynomial Approximation of Conic Sections

In this paper, we obtain explicit representations of several multivariate functions in the Tensor Train (TT) format and explicit TT-representations of tensors that stem from the tensorization of univariate functions on grids. Previous results contained only estimates on the number of parameters (tensor ranks), and this paper fills this gap by providing explicit low-parametric representations for these functions and tensors.     

Probing new top physics at the LHCb experiment

We suggest that top quark physics can be studied at the LHCb experiment and that top quark production could be observed. Since LHCb covers a large pseudorapidity region in the forward direction, it has unique abilities to probe new physics in the top quark sector. Furthermore, we demonstrate that LHCb may be able to measure a t ?t production rate asymmetry and, thus, indirectly probe an anomalous forward-backward t ?t asymmetry in the forward region, a possibility suggested by the enhanced forward-backward asymmetry reported by the CDF experiment.     

Synthesis and structure of novel (S)-1,6-dialkylpiperazine-2,5-diones and (3S,6S)-1,3,6-trialkylpiperazine-2,5-diones

Eleven (S)-1,6-dialkylpiperazine-2,5-diones and five (3S,6S)-1,3,6-trialkylpiperazine-2,5-diones were prepared in three steps from the corresponding (S)-α-amino acid esters comprising of reductive N-alkylation, N-acylation and cyclisation. The synthesis of (S)-1,6-dialkylpiperazine-2,5-diones has a broad scope allowing preparation of diketopiperazines with primary and secondary alkyl groups at N(1), while the synthesis of (3S,6S)-1,3,6-trialkylpiperazine-2,5-diones is limited to compounds with primary alkyl groups at N(1). Reductive alkylation of amino acid ester hydrochlorides by catalytic hydrogenation in the presence of a carbonyl compound proved to be a simple, efficient and general method for the preparation of stable (storable) α-alkylamino acid ester hydrochlorides. The structures of the novel compounds were determined by NMR and X-ray diffraction.     

Oxidative Halogenation with “Green” Oxidants: Oxygen and Hydrogen Peroxide

It is difficult to imagine organic chemistry without organo‐halogen compounds and the molecular halogens needed for their preparation. The halogens have very different reactivity, with iodine usually requiring some form of activation, while others are reactive and hazardous chemicals. To avoid their use, various modified reagents have been discovered (N‐bromo‐ and N‐chlorosuccinimide, Selectfluor…?), but halogens are used to prepare these reagents and when they are used the atom economy is poor. A better approach, which is based on biomimetric research on oxidative halogenation in nature, consists of generating the halogenating reagent in situ under acidic conditions from a halide salt. The result of such a reaction has been halogenation with 100 % halogen atom economy. Suitable oxidants for the oxidation of halides are hydrogen peroxide and oxygen.     

Identification of hydrogen bond modes in polarized Raman spectra of single crystals of α‐oxalic acid dihydrate

Polarized Raman spectra of single crystals of the α‐polymorphs of protonated and deuterated oxalic acid dihydrate were recorded. The interpretation of the spectra is assisted by periodic DFT calculations using the CRYSTAL06 program and by comparison with the infrared spectra of the polycrystalline material. The agreement between the calculated and observed band wavenumbers is fair in the case of low‐anharmonicity modes, but marked differences appear for the stretching modes that are strongly anharmonic. A very broad feature, extending between ∼2000 and 1200 cm⁻¹, is attributed to OH stretching. Notable is the topping of this feature by distinct bands that can be attributed to CO stretching, H₂O scissoring and COH bending coupled to C O stretching. The assignments are supported by isotope effects. However, deuteration does not notably affect the wavenumber limits of the broad OH stretching band, which suggests that the potential governing the proton dynamics is of the asymmetric double‐minimum type with a very low barrier. The calculated normal coordinates show a strong participation of the bending modes of water molecules in almost all internal acid motions, as well as in the external phonons. Copyright © 2009 John Wiley & Sons, Ltd.     

Free radical bromination by the H2O2-HBr system on water

An aqueous solution of hydrogen peroxide and hydrogen bromide illuminated by a 40 W incandescent light bulb serves as a source of bromine radicals. Various substituted toluenes (H, Me, tBu, Br, COOEt, COPh, NO₂) were brominated at the benzyl position. This haloperoxidase-like system for benzylic bromination does not require the presence of metal ions or an organic solvent for efficient conversion of methyl-arenes to benzyl bromides.     

Determination of abamectin and doramectin in sheep faeces using HPLC with fluorescence detection

An analytical procedure for the determination of abamectin and/or doramectin in sheep faeces has been developed. Avermectins were extracted from sheep faeces with acetonitrile, clean-up using solid phase extraction (SPE) and analysed by high performance liquid chromatography (HPLC) with fl uorescence detection after derivatization with N-methylimidazole.The method has a low detection limit (1.0 ng/g of moist sheep faeces), low quanti fi cation limit (2.5 ng/g of moist sheep faeces), good recovery in the range 66.4-80.8% for abamectin and 67.7-85.5% for doramectin as well as good repeatability (>85%). The method is applicable to the study of the time pro fi le of excretion in sheep faeces and also for ecotoxicological studies of both avermectins.     

Proton dynamics in the strong chelate hydrogen bond of crystalline picolinic acid N-oxide. A new computational approach and infrared, raman and INS study

Infrared, Raman and INS spectra of picolinic acid N-oxide (PANO) were recorded and examined for the location of the hydronic modes, particularly O-H stretching and COH bending. PANO is representative of strong chelate hydrogen bonds (H-bonds) with its short O...O distance (2.425 A). H-bonding is possibly well-characterized by diffraction, NMR and NQR data and calculated potential energy functions. The analysis of the spectra is assisted by DFT frequency calculations both in the gas phase and in the solid state. The Car-Parrinello quantum mechanical solid-state method is also used for the proton dynamics simulation; it shows the hydron to be located about 99% of time in the energy minimum near the carboxylic oxygen; jumps to the N-O acceptor are rare. The infrared spectrum excels by an extended absorption (Zundel's continuum) interrupted by numerous Evans transmissions. The model proton potential functions on which the theories of continuum formation are based do not correspond to the experimental and computed characteristics of the hydrogen bond in PANO, therefore a novel approach has been developed; it is based on crystal dynamics driven hydronium potential fluctuation. The envelope of one hundred 0 --> 1 OH stretching transitions generated by molecular dynamics simulation exhibits a maximum at 1400 cm-1 and a minor hump at approximately 1600 cm-1. These positions square well with ones predicted for the COH bending and OH stretching frequencies derived from various one- and two-dimensional model potentials. The coincidences with experimental features have to be considered with caution because the CPMD transition envelope is based solely on the OH stretching coordinate while the observed infrared bands correspond to heavily mixed modes as was previously shown by the normal coordinate analysis of the IR spectrum of argon matrix isolated PANO, the present CPMD frequency calculation and the empirical analysis of spectra. The experimental infrared spectra show some unusual characteristics such as large temperature effects on the intensity of some bands, thus presenting a challenge for theoretical band shape treatments. Our calculations clearly show that the present system is characterized by an asymmetric single well potential with no large amplitudes in the hydronium motion, which extends the existence of Zundel-type spectra beyond the established set of hydrogen bonds with large hydronic vibrational amplitudes.